The derivative expansion in asymptotically safe quantum gravity: general  setup and quartic order

Knorr, Benjamin

doi:10.21468/scipostphyscore.4.3.020

“…The main task here is the evaluation of the trace appearing on the right-hand side of the flow equation (2.2). This can be achieved by means of the universal RG machine developed in [30] and recently upgraded in [199]. The core idea is to use the choices of gauge, background, and regulator together with suitable algebraic manipulations to cast the operator that we want to trace into a form where standard heat-kernel techniques can be applied.…”

Section: Evaluating the Flow Equationmentioning

confidence: 99%

Scalar-tensor theories within Asymptotic Safety

Laporte

¹

,

Pereira

²

,

Saueressig

³

et al. 2021

J. High Energ. Phys.

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Asymptotic Safety provides an elegant mechanism for obtaining a consistent high-energy completion of gravity and gravity-matter systems. Following the initial idea by Steven Weinberg, the construction builds on an interacting fixed point of the theories renormalization group (RG) flow. In this work we use the Wetterich equation for the effective average action to investigate the RG flow of gravity supplemented by a real scalar field. We give a non-perturbative proof that the subspace of interactions respecting the global shift-symmetry of the scalar kinetic term is closed under RG transformations. Subsequently, we compute the beta functions in an approximation comprising the Einstein-Hilbert action supplemented by the shift-symmetric quartic scalar self-interaction and the two lowest order shift-symmetric interactions coupling scalar-bilinears to the spacetime curvature. The computation utilizes the background field method with an arbitrary background, demonstrating that the results are manifestly background independent. Our beta functions exhibit an interacting fixed point suitable for Asymptotic Safety, where all matter interactions are non-vanishing. The presence of this fixed point is rooted in the interplay of the matter couplings which our work tracks for the first time. The relation of our findings with previous results in the literature is discussed in detail and we conclude with a brief outlook on potential phenomenological applications.

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“…The main task here is the evaluation of the trace appearing on the right-hand side of the flow equation (2.2). This can be achieved by means of the universal RG machine developed in [44] and recently upgraded in [195]. The core idea is to use the choices of gauge, background, and regulator together with suitable algebraic manipulations to cast the operator that we want to trace into a form where standard heat-kernel techniques can be applied.…”

Section: Evaluating the Flow Equationmentioning

confidence: 99%

Scalar-Tensor theories within Asymptotic Safety

Laporte,

Pereira,

Saueressig

et al. 2021

Preprint

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Asymptotic Safety provides an elegant mechanism for obtaining a consistent high-energy completion of gravity and gravity-matter systems. Following the initial idea by Steven Weinberg, the construction builds on an interacting fixed point of the theories renormalization group (RG) flow. In this work we use the Wetterich equation for the effective average action to investigate the RG flow of gravity supplemented by a real scalar field. We give a non-perturbative proof that the subspace of interactions respecting the global shift-symmetry of the scalar kinetic term is closed under RG transformations. Subsequently, we compute the beta functions in an approximation comprising the Einstein-Hilbert action supplemented by the shift-symmetric quartic scalar self-interaction and the two lowest order shift-symmetric interactions coupling scalar-bilinears to the spacetime curvature. The computation utilizes the background field method with an arbitrary background, demonstrating that the results are manifestly background independent. Our beta functions exhibit an interacting fixed point suitable for Asymptotic Safety, where all matter interactions are non-vanishing. The presence of this fixed point is rooted in the interplay of the matter couplings which our work tracks for the first time. The relation of our findings with previous results in the literature is discussed in detail and we conclude with a brief outlook on potential phenomenological applications.

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“…Yet, it is of course crucial to supplement the analysis by the actual fixed-point values for G and Λ to discover whether or not asymptotic safety evades the weak-gravity bound and passes this critical viability test. The existence of a fixed point for pure gravity has been established in numerous works [70,72,74, and under the inclusion of matter in [14,28,42,54,75,76,138,[143][144][145][146][147][148][149][150][151][152][153][154][155]. To search for fixed points, we use the beta-functions for Λ and G [156], supplemented with the matter contributions from [144,147].…”

Section: Gravitational Fixed-point Values In Relation To the Weak-gra...mentioning

confidence: 99%

“…We neglect the operators Fµν F µν and Fµν 2 F µν here, which would contribute to the momentumdependent anomalous dimension of the gauge field, see[72] 9. In the presence of diffeomorphism symmetry breaking by the regulator and gauge fixing, there is more than one "avatar" of the Newton coupling.…”

mentioning

confidence: 99%

The weak-gravity bound in asymptotically safe gravity-gauge systems

Eichhorn,

Kwapisz,

Schiffer

2021

Preprint

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The weak-gravity bound has been discovered in asymptotically safe gravitymatter systems, where it limits the maximum strength of gravitational fluctuations. In the present paper, we explore it for the first time in systems with more than one gauge field, to discover whether systems with 12 gauge fields (like the Standard Model) exhibit a weak-gravity bound and whether the gravitational fixed point evades it. Further, we test the robustness of the present and previous results on the weak-gravity bound by exploring their dependence on a gravitational gauge parameter. Finally, the existence of the weak-gravity bound also has important phenomenological consequences: it is key to a proposed mechanism that bounds the spacetime dimensionality from above to four or five dimensions. In this paper, we strengthen the evidence for this mechanism. Thus, the predictive power of the asymptotic safety paradigm could extend to parameters of the spacetime geometry, such that the four-dimensionality of our universe could be explained from first principles.

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The derivative expansion in asymptotically safe quantum gravity: general setup and quartic order

Cited by 39 publications

References 170 publications

Scalar-tensor theories within Asymptotic Safety

Scalar-tensor theories within Asymptotic Safety

Scalar-Tensor theories within Asymptotic Safety

The weak-gravity bound in asymptotically safe gravity-gauge systems

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